I doubt that the official VOA policy in Hainan is similar to that reported in the referenced website (provincial governments do not set visa policy, so you need to find a more reliable source in any event... such as TIMATIC; delta.com hosts a free TIMATIC interface). But, I could be wrong because policies change frequently.

Another pressing matter is that since you'll be arriving on a domestic flight: 1) your 24 hour clock starts the moment you clear border control in Guangzhou, 2) requires that you need to leave China before it is up, and 3) I assume that arrival visas/waivers are issued prior to border control in Sanya/Haikou, which means you might not have access to these facilities landside. Again, there could be a workaround to this issue, assuming VOA is the flavor of the day, but I wouldn't assume such in the absence of proof.

You seem to be working under the assumption that Hainan is not part of "Mainland China" simply because it is an island. This, I can assure you, is categorically incorrect. It answers to Beijing, and the buck stops there.

ETA: I haven't been able to access TIMATIC because my internet is crap here, but everything else I've been able to find (e.g. embassy websites) suggests that the "tour group" requirement still exists. This means "official" Chinese government sanctioned tour... very few travel agents outside of China are government sanctioned (CITIC Travel is an exception that comes to mind, but they get a free pass because they are part of the government).